Beyond a Reasonable Scout - S5-E3
Stupidity: Phil the Scout ties a rope to Mikey's see-saw end's handle to lower Gus down without hurting him. Couldn't Mikey just climb off and hold the see-saw down with his hands and lowered Gus's end down slowly?
The Succubus (a.k.a. Chef's Mama) - S3-E3
Stupidity: When Kenny and Cartman are sitting on the bench, Cartman can't start the tape as he has fallen asleep. Kenny then tries to wake him up, but wouldn't it have made far more sense for him to just start it himself, as he is sitting right next to it? Cartman's job was to push the play button. It was not like he had to rewind, fast forward or even eject the tape, so all Kenny had to do was just simply push the play button and tape would have started to play.
Magical Express Murder Case: File 2 - S2-E11
Stupidity: Kindaichi's logic as usual proves to be right, however, the theater is surrounded by a pond, not the ocean. The investigation proceeds assuming that the killer who performed a meticulously premeditated murder with great knowledge of technology and conjuring, could never go past a bit of water. Likewise, they say "nobody left their seats since the lights go off", as a certainty, but watching the scene and how it unfolds, it's simply an assumption the plot needs.
Stupidity: The master goes through all the trouble of making Luke the vessel so Luke can go and kill several people and risk getting the attention of the slayer, when all he had to do is have his minions go out and kidnap a bunch of people and bring them to him and he could've fed off them himself.
Stupidity: Some ancient advanced civilization took to the task of building this amazing net of stargates that enables instantaneous traveling over hundreds of light years or more, but any stargate can be disabled by anybody just by covering it with dirt or rocks. Apparently if the stargate is buried then it becomes inactive. See Season 1 EP.1.
Suggested correction: This is just you having a different opinion on how the Stargates should work. In fact, the ability to make a Stargate inactive by burying it is a brilliant move by the Ancients. Burying the gate, or even creating a barrier, prevents enemies (like the Goa'uld) from having a convenient way of invading a planet. Although some races, like The Nox, show the ability to activate a Stargate without having to form an unstable vortex.
It's Not Easy Being Green - S5-E16
Stupidity: Unless the tow truck was someone else's or Hank had the keys surely Dale and Bill could've used it to drive Boomhauer's car back.
Stupidity: At the start of the episode, the Brunnen-G planet is about to be under attack by His Shadow in a big ship that is capable of destroying the surface of the planet and everybody on it in under a minute with its fire power. It seems the Brunnen-G had time to respond, seeing as they send a counter measure against His Shadow... Except that they only send a single squadron of 6 fighters. Their planet is about to be obliterated by His Shadow's killer ship, and they only send up 6 fighters. And of course, they fail and all die except for Kai. (00:01:45)